Plan:
- Questions
- The story of the cubic
Discussion:
The discussion page can be found here, for observations and remarks.
Here's a link to Barry Mazur's Imagining Numbers (particularly the square root of minus fifteen): http://www.amazon.com/Imagining-Numbers-particularly-square-fifteen/dp/0312421877/ref=sr_1_1?s=books&ie=UTF8&qid=1364930001&sr=1-1&keywords=barry+mazur
It's only $12. Read the reviews and decide if it's for you.
Typical cubic equation: $ax^3 +bx^2 + cx +d$
Cardono's solution to: $x^3 = cx+d$ (The rule and examples are found on pg 230 of the text)
if:${( \frac{c}{3})}^3 \leq {( \frac{d}{2})}^2$ do the following steps:
$\\ 1. {( \frac{d}{2})}^2 - {( \frac{c}{3})}^3 \\ 2. \sqrt{{( \frac{d}{2})}^2 - {( \frac{c}{3})}^3} \\ 3. \sqrt[3] {d/2 - \sqrt{ {( \frac{d}{2})}^2 - {( \frac{c}{3})}^3}}=u \\ 4. \sqrt[3] {d/2 + \sqrt{ {( \frac{d}{2})}^2 - { ( \frac{c}{3})}^3}}=v \\ 5. x= u+v$
Note that this is only one solution to the equation and it is possible that there are others